[dragonwriter]

> Until now there was no such correlation with Alzeimher's and Fungi.

The point of the criticism seems to be that with an improper control group, there still isn't such a correlation, just a suggestion of a possibility of a correlation. But it might be a correlation between, e.g., age and fungal infection.

That's why, but for the variables under study, you want your control group to look as much like your experimental group as possible.

[philipov]

A general correlation between age and fungal infection might be even more significant, since that suggests a path to reduce the effects of aging in general. Either way, a follow-up study to remove those control flaws and hone in on the cause would be necessary.

[nickff]

Even with an improper control group, the fungi-Alzheimer's correlation still exists. There may be another factor which is causing the correlation (a so-called 'dreaded third thing'), and the correlation may not indicate causation, but the correlation still exists.

[Dylan16807]

That's not how correlations work.

[calinet6]

That is how correlations may not work, though.